In-class Exercise 4: 2nd Order Spatial Point Patterns Analysis Methods

Published

January 30, 2023

Modified

February 6, 2023

1 Overview

This is a continuation of Hands-on Exercise 3. Please refer to Hands-on Exercise 3 for overview of Spatial Point Pattern Analysis and goals of this exercise.

Sections from Datasets to Geospatial Data Wrangling will be the same as Hands-on Exercise 3.

2 Datasets

  • CHILDCARE

    a point feature data providing both location and attribute information of childcare centres. It was downloaded from Data.gov.sg and is in geojson format.

  • MP14_SUBZONE_WEB_PL

    a polygon feature data providing information of URA 2014 Master Plan Planning Subzone boundary data. It is in ESRI shapefile format. This data set was also downloaded from Data.gov.sg.

  • CostalOutline

    a polygon feature data showing the national boundary of Singapore. It is provided by SLA and is in ESRI shapefile format.

3 Installing and Loading R Packages

In this hands-on exercise, five R packages will be used, they are:

  • sf, a relatively new R package specially designed to import, manage and process vector-based geospatial data in R.
  • spatstat, which has a wide range of useful functions for point pattern analysis. In this hands-on exercise, it will be used to perform 1st- and 2nd-order spatial point patterns analysis and derive kernel density estimation (KDE) layer.
  • raster which reads, writes, manipulates, analyses and model of gridded spatial data (i.e. raster). In this hands-on exercise, it will be used to convert image output generate by spatstat into raster format.
  • maptools which provides a set of tools for manipulating geographic data. In this hands-on exercise, we mainly use it to convert Spatial objects into ppp format (i.e., representing a point pattern dataset in the two-dimensional plane) of spatstat.
  • tmap which provides functions for plotting cartographic quality static point patterns maps or interactive maps by using leaflet API.
pacman::p_load(sf, spatstat, raster, maptools, tmap)

4 Spatial Data Wrangling

4.1 Importing Spatial Data

In this section, st_read() of sf package will be used to import these three geospatial data sets into R.

Locations and Attributes of Childcare Centres

childcare_sf <- st_read("data/child-care-services-geojson.geojson") %>% 
  st_transform(crs = 3414)
Reading layer `child-care-services-geojson' from data source 
  `C:\deadline2359\IS415-GAA\In-class_Ex\In-class_Ex04\data\child-care-services-geojson.geojson' 
  using driver `GeoJSON'
Simple feature collection with 1545 features and 2 fields
Geometry type: POINT
Dimension:     XYZ
Bounding box:  xmin: 103.6824 ymin: 1.248403 xmax: 103.9897 ymax: 1.462134
z_range:       zmin: 0 zmax: 0
Geodetic CRS:  WGS 84

URA 2014 Master Plan Planning Subzone Boundaries

mpsz_sf <- st_read(dsn = "data",
                   layer = "MP14_SUBZONE_WEB_PL")
Reading layer `MP14_SUBZONE_WEB_PL' from data source 
  `C:\deadline2359\IS415-GAA\In-class_Ex\In-class_Ex04\data' 
  using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21

National Boundary of Singapore

sg_sf <- st_read(dsn = "data",
                 layer = "CostalOutline")
Reading layer `CostalOutline' from data source 
  `C:\deadline2359\IS415-GAA\In-class_Ex\In-class_Ex04\data' 
  using driver `ESRI Shapefile'
Simple feature collection with 60 features and 4 fields
Geometry type: POLYGON
Dimension:     XY
Bounding box:  xmin: 2663.926 ymin: 16357.98 xmax: 56047.79 ymax: 50244.03
Projected CRS: SVY21

4.1.1 Map Projection

Before we can use these data for analysis, it is important for us to ensure that they are projected in same projection system.

DIY: Using the appropriate sf function you learned in Hands-on Exercise 2, retrieve the referencing system information of these geospatial data.

st_crs(childcare_sf)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]
st_crs(mpsz_sf)
Coordinate Reference System:
  User input: SVY21 
  wkt:
PROJCRS["SVY21",
    BASEGEOGCRS["SVY21[WGS84]",
        DATUM["World Geodetic System 1984",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]],
            ID["EPSG",6326]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["Degree",0.0174532925199433]]],
    CONVERSION["unnamed",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["(E)",east,
            ORDER[1],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]],
        AXIS["(N)",north,
            ORDER[2],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]]]
st_crs(sg_sf)
Coordinate Reference System:
  User input: SVY21 
  wkt:
PROJCRS["SVY21",
    BASEGEOGCRS["SVY21[WGS84]",
        DATUM["World Geodetic System 1984",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]],
            ID["EPSG",6326]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["Degree",0.0174532925199433]]],
    CONVERSION["unnamed",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["(E)",east,
            ORDER[1],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]],
        AXIS["(N)",north,
            ORDER[2],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]]]

Notice that except childcare_sf, both mpsz_sf and sg_sf do not have proper CRS information.

Hence, the correct CRS (i.e., 3414) needs to be assigned to mpsz_sf and sg_sf simple feature data frames.

mpsz_sf <- st_set_crs(mpsz_sf, 3414)
st_crs(mpsz_sf)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]
sg_sf <- st_set_crs(sg_sf, 3414)
st_crs(sg_sf)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]

4.2 Mapping Geospatial Datasets

After checking the referencing system of each geospatial data data frame, it is also useful for us to plot a map to show their spatial patterns.

tm_shape(mpsz_sf) +
  tm_polygons() +
tm_shape(childcare_sf) +
  tm_symbols(size = 0.02, col = "black")

Notice that all the geospatial layers are within the same map extend. This shows that their referencing system and coordinate values are referred to similar spatial context. This is very important in any geospatial analysis.

Alternatively, a pin map can be prepared by using the code chunk below.

tmap_mode("view") # interactive
tm_shape(childcare_sf) +
  tm_dots()
tmap_mode("plot") # return to default

Notice that in interactive mode, tmap is using leaflet for R API. The advantage of this interactive pin map is it allows us to navigate and zoom around the map freely. We can also query the information of each simple feature (i.e. the point) by clicking of them. Last but not least, you can also change the background of the internet map layer.

Currently, three internet map layers are provided. They are: ESRI.WorldGrayCanvas (default), OpenStreetMap, and ESRI.WorldTopoMap.

Warning

Always remember to switch back to plot mode after creating an interactive map. This is because, each interactive mode will consume a connection. You should also avoid displaying excessive numbers of interactive maps (i.e., not more than 10) in one RMarkdown document when publish on Netlify.

5 Geospatial Data Wrangling

Although simple feature data frame is gaining popularity against sp’s Spatial* classes, many geospatial analysis packages still require the input geospatial data be in sp’s Spatial* classes.

5.1 Converting sf data frames to sp’s Spatial* class

Converting sf DataFrames to sp’s Spatial* Class

The code chunk below uses as_Spatial() of sf package to convert the three geospatial data from simple feature data frame to sp’s Spatial* class.

childcare <- as_Spatial(childcare_sf)
mpsz <- as_Spatial(mpsz_sf)
sg <- as_Spatial(sg_sf)

The following are the information of the three Spatial* classes.

childcare
class       : SpatialPointsDataFrame 
features    : 1545 
extent      : 11203.01, 45404.24, 25667.6, 49300.88  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 
variables   : 2
names       :    Name,                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Description 
min values  :   kml_1, <center><table><tr><th colspan='2' align='center'><em>Attributes</em></th></tr><tr bgcolor="#E3E3F3"> <th>ADDRESSBLOCKHOUSENUMBER</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSBUILDINGNAME</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSPOSTALCODE</th> <td>018989</td> </tr><tr bgcolor=""> <th>ADDRESSSTREETNAME</th> <td>1, MARINA BOULEVARD, #B1 - 01, ONE MARINA BOULEVARD, SINGAPORE 018989</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSTYPE</th> <td></td> </tr><tr bgcolor=""> <th>DESCRIPTION</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>HYPERLINK</th> <td></td> </tr><tr bgcolor=""> <th>LANDXADDRESSPOINT</th> <td>0</td> </tr><tr bgcolor="#E3E3F3"> <th>LANDYADDRESSPOINT</th> <td>0</td> </tr><tr bgcolor=""> <th>NAME</th> <td>THE LITTLE SKOOL-HOUSE INTERNATIONAL PTE. LTD.</td> </tr><tr bgcolor="#E3E3F3"> <th>PHOTOURL</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSFLOORNUMBER</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>INC_CRC</th> <td>08F73931F4A691F4</td> </tr><tr bgcolor=""> <th>FMEL_UPD_D</th> <td>20200826094036</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSUNITNUMBER</th> <td></td> </tr></table></center> 
max values  : kml_999,                  <center><table><tr><th colspan='2' align='center'><em>Attributes</em></th></tr><tr bgcolor="#E3E3F3"> <th>ADDRESSBLOCKHOUSENUMBER</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSBUILDINGNAME</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSPOSTALCODE</th> <td>829646</td> </tr><tr bgcolor=""> <th>ADDRESSSTREETNAME</th> <td>200, PONGGOL SEVENTEENTH AVENUE, SINGAPORE 829646</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSTYPE</th> <td></td> </tr><tr bgcolor=""> <th>DESCRIPTION</th> <td>Child Care Services</td> </tr><tr bgcolor="#E3E3F3"> <th>HYPERLINK</th> <td></td> </tr><tr bgcolor=""> <th>LANDXADDRESSPOINT</th> <td>0</td> </tr><tr bgcolor="#E3E3F3"> <th>LANDYADDRESSPOINT</th> <td>0</td> </tr><tr bgcolor=""> <th>NAME</th> <td>RAFFLES KIDZ @ PUNGGOL PTE LTD</td> </tr><tr bgcolor="#E3E3F3"> <th>PHOTOURL</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSFLOORNUMBER</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>INC_CRC</th> <td>379D017BF244B0FA</td> </tr><tr bgcolor=""> <th>FMEL_UPD_D</th> <td>20200826094036</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSUNITNUMBER</th> <td></td> </tr></table></center> 
mpsz
class       : SpatialPolygonsDataFrame 
features    : 323 
extent      : 2667.538, 56396.44, 15748.72, 50256.33  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 
variables   : 15
names       : OBJECTID, SUBZONE_NO, SUBZONE_N, SUBZONE_C, CA_IND, PLN_AREA_N, PLN_AREA_C,       REGION_N, REGION_C,          INC_CRC, FMEL_UPD_D,     X_ADDR,     Y_ADDR,    SHAPE_Leng,    SHAPE_Area 
min values  :        1,          1, ADMIRALTY,    AMSZ01,      N, ANG MO KIO,         AM, CENTRAL REGION,       CR, 00F5E30B5C9B7AD8,      16409,  5092.8949,  19579.069, 871.554887798, 39437.9352703 
max values  :      323,         17,    YUNNAN,    YSSZ09,      Y,     YISHUN,         YS,    WEST REGION,       WR, FFCCF172717C2EAF,      16409, 50424.7923, 49552.7904, 68083.9364708,  69748298.792 
sg
class       : SpatialPolygonsDataFrame 
features    : 60 
extent      : 2663.926, 56047.79, 16357.98, 50244.03  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 
variables   : 4
names       : GDO_GID, MSLINK, MAPID,              COSTAL_NAM 
min values  :       1,      1,     0,             ISLAND LINK 
max values  :      60,     67,     0, SINGAPORE - MAIN ISLAND

5.2 Converting Spatial* Class into Generic sp Format

spatstat requires the analytical data in ppp object form. There is no direct way to convert a Spatial* classes into ppp object. We need to convert the Spatial classes* into Spatial object first.

The codes chunk below converts the Spatial* classes into generic sp objects.

childcare_sp <- as(childcare, "SpatialPoints")
sg_sp <- as(sg, "SpatialPolygons")

The properties of the sp objects are as follow:

childcare_sp
class       : SpatialPoints 
features    : 1545 
extent      : 11203.01, 45404.24, 25667.6, 49300.88  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 
sg_sp
class       : SpatialPolygons 
features    : 60 
extent      : 2663.926, 56047.79, 16357.98, 50244.03  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs

5.3 Converting Generic sp Format into spatstat’s ppp Format

Now, we will use as.ppp() function of spatstat to convert the spatial data into spatstat’s ppp object format.

childcare_ppp <- as(childcare_sp, "ppp")
childcare_ppp
Planar point pattern: 1545 points
window: rectangle = [11203.01, 45404.24] x [25667.6, 49300.88] units
plot(childcare_ppp)

Below shows the summary statistics of the childcare_ppp object.

summary(childcare_ppp)
Planar point pattern:  1545 points
Average intensity 1.91145e-06 points per square unit

*Pattern contains duplicated points*

Coordinates are given to 3 decimal places
i.e. rounded to the nearest multiple of 0.001 units

Window: rectangle = [11203.01, 45404.24] x [25667.6, 49300.88] units
                    (34200 x 23630 units)
Window area = 808287000 square units
Note

Notice the warning message about duplicates. In spatial point patterns analysis, an issue of significant is the presence of duplicates. The statistical methodology used for spatial point patterns processes is based largely on the assumption that process are simple, that is, that the points cannot be coincident.

5.4 Handling Duplicated Points

The duplication in a ppp object can be checked by using the code chunk below.

any(duplicated(childcare_ppp))
[1] TRUE

To count the number of co-indicence point, the multiplicity() function can be used as shown below.

multiplicity(childcare_ppp)

If we want to know how many locations have more than one point event, we can use the code chunk below.

sum(multiplicity(childcare_ppp) > 1)
[1] 128

The output shows that there are 128 duplicated point events.

To view the locations of these duplicate point events, we will plot childcare data by using the code chunk below.

tmap_mode("view")
tm_shape(childcare) +
  tm_dots(alpha = 0.4,
          size = 0.05)
tmap_mode("plot")

There are three ways to overcome this problem.

  1. The easiest way is to delete the duplicates. But, that will also mean that some useful point events will be lost.
  2. The second solution is use jittering, which will add a small perturbation to the duplicate points so that they do not occupy the exact same space.
  3. The third solution is to make each point “unique” and then attach the duplicates of the points to the patterns as marks, as attributes of the points. Then you would need analytical techniques that take into account these marks.

The code chunk below implements the jittering approach.

childcare_ppp_jit <- rjitter(childcare_ppp,
                             # Whether to retry when a perturbed point lies outside the window of the original point pattern
                             retry = TRUE,
                             # No. of simulated realisations to be generated
                             nsim = 1, 
                             #  If nsim=1 and drop=TRUE, the result will be a point pattern, rather than a list containing a point pattern.
                             drop = TRUE)

Again, to check if any duplicated point remains in the geospatial data.

any(duplicated(childcare_ppp_jit))
[1] FALSE

5.5 Creating owin Object

When analysing spatial point patterns, it is a good practice to confine the analysis with a geographical area like Singapore boundary. In spatstat, an object called owin is specially designed to represent this polygonal region.

The code chunk below is used to covert sg SpatialPolygon object into owin object of spatstat.

sg_owin <- as(sg_sp, "owin")

The ouput object can be displayed by using plot() function

plot(sg_owin)

and summary() function of Base R.

summary(sg_owin)
Window: polygonal boundary
60 separate polygons (no holes)
            vertices        area relative.area
polygon 1         38 1.56140e+04      2.09e-05
polygon 2        735 4.69093e+06      6.27e-03
polygon 3         49 1.66986e+04      2.23e-05
polygon 4         76 3.12332e+05      4.17e-04
polygon 5       5141 6.36179e+08      8.50e-01
polygon 6         42 5.58317e+04      7.46e-05
polygon 7         67 1.31354e+06      1.75e-03
polygon 8         15 4.46420e+03      5.96e-06
polygon 9         14 5.46674e+03      7.30e-06
polygon 10        37 5.26194e+03      7.03e-06
polygon 11        53 3.44003e+04      4.59e-05
polygon 12        74 5.82234e+04      7.78e-05
polygon 13        69 5.63134e+04      7.52e-05
polygon 14       143 1.45139e+05      1.94e-04
polygon 15       165 3.38736e+05      4.52e-04
polygon 16       130 9.40465e+04      1.26e-04
polygon 17        19 1.80977e+03      2.42e-06
polygon 18        16 2.01046e+03      2.69e-06
polygon 19        93 4.30642e+05      5.75e-04
polygon 20        90 4.15092e+05      5.54e-04
polygon 21       721 1.92795e+06      2.57e-03
polygon 22       330 1.11896e+06      1.49e-03
polygon 23       115 9.28394e+05      1.24e-03
polygon 24        37 1.01705e+04      1.36e-05
polygon 25        25 1.66227e+04      2.22e-05
polygon 26        10 2.14507e+03      2.86e-06
polygon 27       190 2.02489e+05      2.70e-04
polygon 28       175 9.25904e+05      1.24e-03
polygon 29      1993 9.99217e+06      1.33e-02
polygon 30        38 2.42492e+04      3.24e-05
polygon 31        24 6.35239e+03      8.48e-06
polygon 32        53 6.35791e+05      8.49e-04
polygon 33        41 1.60161e+04      2.14e-05
polygon 34        22 2.54368e+03      3.40e-06
polygon 35        30 1.08382e+04      1.45e-05
polygon 36       327 2.16921e+06      2.90e-03
polygon 37       111 6.62927e+05      8.85e-04
polygon 38        90 1.15991e+05      1.55e-04
polygon 39        98 6.26829e+04      8.37e-05
polygon 40       415 3.25384e+06      4.35e-03
polygon 41       222 1.51142e+06      2.02e-03
polygon 42       107 6.33039e+05      8.45e-04
polygon 43         7 2.48299e+03      3.32e-06
polygon 44        17 3.28303e+04      4.38e-05
polygon 45        26 8.34758e+03      1.11e-05
polygon 46       177 4.67446e+05      6.24e-04
polygon 47        16 3.19460e+03      4.27e-06
polygon 48        15 4.87296e+03      6.51e-06
polygon 49        66 1.61841e+04      2.16e-05
polygon 50       149 5.63430e+06      7.53e-03
polygon 51       609 2.62570e+07      3.51e-02
polygon 52         8 7.82256e+03      1.04e-05
polygon 53       976 2.33447e+07      3.12e-02
polygon 54        55 8.25379e+04      1.10e-04
polygon 55       976 2.33447e+07      3.12e-02
polygon 56        61 3.33449e+05      4.45e-04
polygon 57         6 1.68410e+04      2.25e-05
polygon 58         4 9.45963e+03      1.26e-05
polygon 59        46 6.99702e+05      9.35e-04
polygon 60        13 7.00873e+04      9.36e-05
enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
                     (53380 x 33890 units)
Window area = 748741000 square units
Fraction of frame area: 0.414

5.6 Combining Point Events Object and owin Object

In this last step of geospatial data wrangling, we will extract childcare events that are located within Singapore by using the code chunk below.

childcareSG_ppp = childcare_ppp[sg_owin]

The output object combined both the point and polygon feature in one ppp object class as shown below.

summary(childcareSG_ppp)
Planar point pattern:  1545 points
Average intensity 2.063463e-06 points per square unit

*Pattern contains duplicated points*

Coordinates are given to 3 decimal places
i.e. rounded to the nearest multiple of 0.001 units

Window: polygonal boundary
60 separate polygons (no holes)
            vertices        area relative.area
polygon 1         38 1.56140e+04      2.09e-05
polygon 2        735 4.69093e+06      6.27e-03
polygon 3         49 1.66986e+04      2.23e-05
polygon 4         76 3.12332e+05      4.17e-04
polygon 5       5141 6.36179e+08      8.50e-01
polygon 6         42 5.58317e+04      7.46e-05
polygon 7         67 1.31354e+06      1.75e-03
polygon 8         15 4.46420e+03      5.96e-06
polygon 9         14 5.46674e+03      7.30e-06
polygon 10        37 5.26194e+03      7.03e-06
polygon 11        53 3.44003e+04      4.59e-05
polygon 12        74 5.82234e+04      7.78e-05
polygon 13        69 5.63134e+04      7.52e-05
polygon 14       143 1.45139e+05      1.94e-04
polygon 15       165 3.38736e+05      4.52e-04
polygon 16       130 9.40465e+04      1.26e-04
polygon 17        19 1.80977e+03      2.42e-06
polygon 18        16 2.01046e+03      2.69e-06
polygon 19        93 4.30642e+05      5.75e-04
polygon 20        90 4.15092e+05      5.54e-04
polygon 21       721 1.92795e+06      2.57e-03
polygon 22       330 1.11896e+06      1.49e-03
polygon 23       115 9.28394e+05      1.24e-03
polygon 24        37 1.01705e+04      1.36e-05
polygon 25        25 1.66227e+04      2.22e-05
polygon 26        10 2.14507e+03      2.86e-06
polygon 27       190 2.02489e+05      2.70e-04
polygon 28       175 9.25904e+05      1.24e-03
polygon 29      1993 9.99217e+06      1.33e-02
polygon 30        38 2.42492e+04      3.24e-05
polygon 31        24 6.35239e+03      8.48e-06
polygon 32        53 6.35791e+05      8.49e-04
polygon 33        41 1.60161e+04      2.14e-05
polygon 34        22 2.54368e+03      3.40e-06
polygon 35        30 1.08382e+04      1.45e-05
polygon 36       327 2.16921e+06      2.90e-03
polygon 37       111 6.62927e+05      8.85e-04
polygon 38        90 1.15991e+05      1.55e-04
polygon 39        98 6.26829e+04      8.37e-05
polygon 40       415 3.25384e+06      4.35e-03
polygon 41       222 1.51142e+06      2.02e-03
polygon 42       107 6.33039e+05      8.45e-04
polygon 43         7 2.48299e+03      3.32e-06
polygon 44        17 3.28303e+04      4.38e-05
polygon 45        26 8.34758e+03      1.11e-05
polygon 46       177 4.67446e+05      6.24e-04
polygon 47        16 3.19460e+03      4.27e-06
polygon 48        15 4.87296e+03      6.51e-06
polygon 49        66 1.61841e+04      2.16e-05
polygon 50       149 5.63430e+06      7.53e-03
polygon 51       609 2.62570e+07      3.51e-02
polygon 52         8 7.82256e+03      1.04e-05
polygon 53       976 2.33447e+07      3.12e-02
polygon 54        55 8.25379e+04      1.10e-04
polygon 55       976 2.33447e+07      3.12e-02
polygon 56        61 3.33449e+05      4.45e-04
polygon 57         6 1.68410e+04      2.25e-05
polygon 58         4 9.45963e+03      1.26e-05
polygon 59        46 6.99702e+05      9.35e-04
polygon 60        13 7.00873e+04      9.36e-05
enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
                     (53380 x 33890 units)
Window area = 748741000 square units
Fraction of frame area: 0.414

Using plot(), the childcareSG_ppp object can be displayed.

plot(childcareSG_ppp)

5.6.1 Extracting Study Area

The below code chunk will be used to extract the target planning areas.

pg = mpsz[mpsz@data$PLN_AREA_N == "PUNGGOL",]
tm = mpsz[mpsz@data$PLN_AREA_N == "TAMPINES",]
ck = mpsz[mpsz@data$PLN_AREA_N == "CHOA CHU KANG",]
jw = mpsz[mpsz@data$PLN_AREA_N == "JURONG WEST",]
par(mfrow=c(2,2))
plot(pg, main = "Punggol")
plot(tm, main = "Tampines")
plot(ck, main = "Choa Chu Kang")
plot(jw, main = "Jurong West")

5.6.2 Converting spatial point data frame into generic sp format

pg_sp = as(pg, "SpatialPolygons")
tm_sp = as(tm, "SpatialPolygons")
ck_sp = as(ck, "SpatialPolygons")
jw_sp = as(jw, "SpatialPolygons")

5.6.3 Creating owin Object

Converting these SpatialPolygons objects into owin objects that is required by spatstat.

pg_owin = as(pg_sp, "owin")
tm_owin = as(tm_sp, "owin")
ck_owin = as(ck_sp, "owin")
jw_owin = as(jw_sp, "owin")

5.6.4 Combining childcare points and study area

Extracting childcare that is within the specific region to do analysis later on.

childcare_pg_ppp = childcare_ppp_jit[pg_owin]
childcare_tm_ppp = childcare_ppp_jit[tm_owin]
childcare_ck_ppp = childcare_ppp_jit[ck_owin]
childcare_jw_ppp = childcare_ppp_jit[jw_owin]

Next, rescale() function is used to covert the unit of measurement from metre to kilometre.

childcare_pg_ppp.km = rescale(childcare_pg_ppp, 1000, "km")
childcare_tm_ppp.km = rescale(childcare_tm_ppp, 1000, "km")
childcare_ck_ppp.km = rescale(childcare_ck_ppp, 1000, "km")
childcare_jw_ppp.km = rescale(childcare_jw_ppp, 1000, "km")

The code chunk below is used to plot these four study areas and the locations of the childcare centres.

par(mfrow=c(2,2))
plot(childcare_pg_ppp.km, main="Punggol")
plot(childcare_tm_ppp.km, main="Tampines")
plot(childcare_ck_ppp.km, main="Choa Chu Kang")
plot(childcare_jw_ppp.km, main="Jurong West")

6 Second-order Spatial Point Patterns Analysis

6.1 Analysing Spatial Point Process Using G-Function

G function measures the distribution of the distances from an arbitrary event to its nearest event (nearest neighbour distance). In this section, G-function estimation can be calculated by using Gest() of spatstat package.Monta carlo simulation test will also be used using envelope() of spatstat package.

6.1.1 Choa Chu Kang planning area

6.1.1.1 Computing G-function estimation

The code chunk below is used to compute G-function using Gest() of spatat package.

G_CK = Gest(childcare_ck_ppp, 
            correction = "border") # edge correction
plot(G_CK, xlim=c(0,500))

6.1.2 Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

  • Ho = The distribution of childcare services at Choa Chu Kang are randomly distributed.

  • H1= The distribution of childcare services at Choa Chu Kang are not randomly distributed.

The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.

Monte Carlo test with G-function

G_CK.csr <- envelope(childcare_ck_ppp, Gest, nsim = 999)
Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60........
.70.........80.........90.........100.........110.........120.........130......
...140.........150.........160.........170.........180.........190.........200....
.....210.........220.........230.........240.........250.........260.........270..
.......280.........290.........300.........310.........320.........330.........340
.........350.........360.........370.........380.........390.........400........
.410.........420.........430.........440.........450.........460.........470......
...480.........490.........500.........510.........520.........530.........540....
.....550.........560.........570.........580.........590.........600.........610..
.......620.........630.........640.........650.........660.........670.........680
.........690.........700.........710.........720.........730.........740........
.750.........760.........770.........780.........790.........800.........810......
...820.........830.........840.........850.........860.........870.........880....
.....890.........900.........910.........920.........930.........940.........950..
.......960.........970.........980.........990........ 999.

Done.
plot(G_CK.csr)

6.1.3 Tampines planning area

6.1.3.1 Computing G-function estimation

G_tm = Gest(childcare_tm_ppp, correction = "best")
plot(G_tm)

6.1.3.2 Performing Complete Spatial Randomness Test

Similar to Choa Chu Kang, hypothesis test needs to be formed and tested to confirm the above spatial patterns.

  • Ho = The distribution of childcare services at Tampines are randomly distributed.

  • H1= The distribution of childcare services at Tampines are not randomly distributed.

G_tm.csr <- envelope(childcare_tm_ppp, Gest, correction = "all", nsim = 999)
Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60........
.70.........80.........90.........100.........110.........120.........130......
...140.........150.........160.........170.........180.........190.........200....
.....210.........220.........230.........240.........250.........260.........270..
.......280.........290.........300.........310.........320.........330.........340
.........350.........360.........370.........380.........390.........400........
.410.........420.........430.........440.........450.........460.........470......
...480.........490.........500.........510.........520.........530.........540....
.....550.........560.........570.........580.........590.........600.........610..
.......620.........630.........640.........650.........660.........670.........680
.........690.........700.........710.........720.........730.........740........
.750.........760.........770.........780.........790.........800.........810......
...820.........830.........840.........850.........860.........870.........880....
.....890.........900.........910.........920.........930.........940.........950..
.......960.........970.........980.........990........ 999.

Done.
plot(G_tm.csr)

6.2 Analysing Spatial Point Process Using F-Function

F function estimates the empty space function F(r) or its hazard rate h(r) from a point pattern in a window of arbitrary shape. In this section, Fest() of spatstat package will be need for F-function estimation. envelope() of spatstat package will continue to be used.

6.2.1 Choa Chu Kang planning area

6.2.1.1 Computing F-function estimation

The code chunk below is used to compute F-function using Fest() of spastat package.

F_CK = Fest(childcare_ck_ppp)
plot(F_CK)

6.2.1.2 Performing Complete Spatial Randomness Test

  • Ho = The distribution of childcare services at Choa Chu Kang are randomly distributed.

  • H1= The distribution of childcare services at Choa Chu Kang are not randomly distributed.

Monte Carlo Test with F-function

F_CK.csr <- envelope(childcare_ck_ppp, Fest, nsim = 999)
Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60........
.70.........80.........90.........100.........110.........120.........130......
...140.........150.........160.........170.........180.........190.........200....
.....210.........220.........230.........240.........250.........260.........270..
.......280.........290.........300.........310.........320.........330.........340
.........350.........360.........370.........380.........390.........400........
.410.........420.........430.........440.........450.........460.........470......
...480.........490.........500.........510.........520.........530.........540....
.....550.........560.........570.........580.........590.........600.........610..
.......620.........630.........640.........650.........660.........670.........680
.........690.........700.........710.........720.........730.........740........
.750.........760.........770.........780.........790.........800.........810......
...820.........830.........840.........850.........860.........870.........880....
.....890.........900.........910.........920.........930.........940.........950..
.......960.........970.........980.........990........ 999.

Done.
plot(F_CK.csr)

6.2.2 Tampines planning area

6.2.2.1 Computing F-function estimation

F_tm = Fest(childcare_tm_ppp, correction = "best")
plot(F_tm)

6.2.2.2 Performing Complete Spatial Randomness Test

  • Ho = The distribution of childcare services at Tampines are randomly distributed.

  • H1= The distribution of childcare services at Tampines are not randomly distributed.

F_tm.csr <- envelope(childcare_tm_ppp, Fest, correction = "all", nsim = 999)
Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60........
.70.........80.........90.........100.........110.........120.........130......
...140.........150.........160.........170.........180.........190.........200....
.....210.........220.........230.........240.........250.........260.........270..
.......280.........290.........300.........310.........320.........330.........340
.........350.........360.........370.........380.........390.........400........
.410.........420.........430.........440.........450.........460.........470......
...480.........490.........500.........510.........520.........530.........540....
.....550.........560.........570.........580.........590.........600.........610..
.......620.........630.........640.........650.........660.........670.........680
.........690.........700.........710.........720.........730.........740........
.750.........760.........770.........780.........790.........800.........810......
...820.........830.........840.........850.........860.........870.........880....
.....890.........900.........910.........920.........930.........940.........950..
.......960.........970.........980.........990........ 999.

Done.
plot(F_tm.csr)

6.3 Analysing Spatial Point Process Using K-Function

K-function measures the number of events found up to a given distance of any particular event. Here, Kest() of spatstat package will be utilised. Again, envelope() of spatstat package is used.

6.3.1 Choa Chu Kang planning area

6.3.1.1 Computing K-function estimate

K_ck = Kest(childcare_ck_ppp, correction = "Ripley")
plot(K_ck, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")

6.3.1.2 Performing Complete Spatial Randomness Test

  • Ho = The distribution of childcare services at Choa Chu Kang are randomly distributed.

  • H1= The distribution of childcare services at Choa Chu Kang are not randomly distributed.

K_ck.csr <- envelope(childcare_ck_ppp, Kest, nsim = 99, rank = 1, glocal=TRUE)
Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,  99.

Done.
plot(K_ck.csr, . - r ~ r, xlab="d", ylab="K(d)-r")

6.3.2 Tampines planning area

6.3.2.1 Computing K-function estimation

K_tm = Kest(childcare_tm_ppp, correction = "Ripley")
plot(K_tm, . -r ~ r, 
     ylab= "K(d)-r", xlab = "d(m)", 
     xlim=c(0,1000))

6.3.2.2 Performing Complete Spatial Randomness Test

  • Ho = The distribution of childcare services at Tampines are randomly distributed.

  • H1= The distribution of childcare services at Tampines are not randomly distributed.

K_tm.csr <- envelope(childcare_tm_ppp, Kest, nsim = 99, rank = 1, glocal=TRUE)
Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,  99.

Done.
plot(K_tm.csr, . - r ~ r, 
     xlab="d", ylab="K(d)-r", xlim=c(0,500))

6.4 Analysing Spatial Point Process Using L-Function

Computation of L-function estimation can be done through using Lest() of spatstat package. And yes, envelope() of spatstat package will be used.

6.4.1 Choa Chu Kang planning area

6.4.1.1 Computing L Function estimation

L_ck = Lest(childcare_ck_ppp, correction = "Ripley")
plot(L_ck, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)")

6.4.1.2 Performing Complete Spatial Randomness Test

  • Ho = The distribution of childcare services at Choa Chu Kang are randomly distributed.

  • H1= The distribution of childcare services at Choa Chu Kang are not randomly distributed.

L_ck.csr <- envelope(childcare_ck_ppp, Lest, nsim = 99, rank = 1, glocal=TRUE)
Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,  99.

Done.
plot(L_ck.csr, . - r ~ r, xlab="d", ylab="L(d)-r")

6.4.2 Tampines planning area

6.4.2.1 Computing L-function estimate

L_tm = Lest(childcare_tm_ppp, correction = "Ripley")
plot(L_tm, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)", 
     xlim=c(0,1000))

6.4.2.2 Performing Complete Spatial Randomness Test

  • Ho = The distribution of childcare services at Tampines are randomly distributed.

  • H1= The distribution of childcare services at Tampines are not randomly distributed.

L_tm.csr <- envelope(childcare_tm_ppp, Lest, nsim = 99, rank = 1, glocal=TRUE)
Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,  99.

Done.
plot(L_tm.csr, . - r ~ r, 
     xlab="d", ylab="L(d)-r", xlim=c(0,500))